Free Vibration Research Articles

Free vibrations analysis of the aircraft IAR-99 HAWK based on a new and modern finite element model

Free vibrations analysis of the aircraft IAR-99 HAWK based on a new and modern finite element model

Nondimensional triply coupled free vibration analysis of the axially layered thin-walled beams with nonsymmetric open cross sections and its application to the frequency optimization

Nondimensional triply coupled free vibration analysis of the axially layered thin-walled beams with nonsymmetric open cross sections and its application to the frequency optimization

Experimental study on the free and constrained vibration performance of composite wave springs

This article proposes a glass fiber reinforced plastic (GFRP) wave spring and conducts a study on its free and constrained vibration characteristics and compression performance. Initially, a stiffness prediction model for composite wave spring is established using laminated plate theory and Moore’s theorem. Additionally, the failure mode of the composite wave spring was predicted and experimentally confirmed using ABAQUS and the 3D-Hashin failure criterion. Finally, the vibration characteristics of composite wave spring and metal helical spring are investigated using the B&K testing system in both free and constrained states. The experimental stiffness and ultimate load of the composite wave spring are 20.67 N/mm and 1386.67 N. The composite wave spring exhibits good vibration reduction performance in both free and constrained states, with maximum vibration attenuation amplitudes of 122.71 and 144.93 dB. In comparison, the metal helical spring has maximum vibration attenuation amplitudes of 41.65 and 111.89 dB.

An exact analytical method for free vibration analysis of FG-GPLRC sector cylindrical shells under Levy-type boundary conditions

In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating the material properties of the graded layers of the shell with three different grading patterns. Mathematical modeling of the Levy-type cylindrical shell is based on the Hamilton principle and the Sanders first-order shear deformation theory (FSDT). The governing equations of the composite shell are analytically solved using the state-space method. The validity of the proposed analytical method is demonstrated by the excellent agreement between the obtained results of the exact analytical solution and the results available in the literature. Furthermore, some parametric studies are conducted to reveal the effects of variations in boundary conditions, GPL distribution patterns, GPL weight fraction, and geometrical parameters such as shallowness angle, length-to-radius ratio, and thickness on the free vibration behavior of the shell structure. Natural frequencies and mode switching are reported for different mode numbers.

Stiffness and damping tuning through using a piezoelectric friction damper and a layered structure

Abstract Vibration suppression is essential for enhancing the performance of mechanical systems, as it prevents structural damage and minimizes noise. Various methods, including passive, semi-active, and active approaches, have been developed to achieve this goal. Among these, friction dampers, primarily categorized as passive, are highly efficient in adjusting system damping and influencing energy dissipation. By modulating the normal force in the friction damper based on external force intensity, performance can be further enhanced. This study employs a piezoelectric actuator to regulate the normal force and introduces an analytical method along with finite element modeling to estimate the normal force in the friction damper. A layered structure is introduced as an additional mean to tune damping and stiffness. The performance of the semi-active piezoelectric friction damper is investigated in free and forced vibrations, including flexural and axial cyclic loads. Furthermore, the advantages of employing layered structures are investigated experimentally. Overall, the piezoelectric friction damper demonstrates effective energy dissipation during macroslip events. Nevertheless, in case of microslip, increasing the actuator voltage results in reduced damping and a marginal rise in stiffness.

Comprehensive Analysis of Static, Buckling, and Free Vibration Behavior of Carbon Nanotube Reinforced Composite Plates on Pasternak’s Elastic Foundation

Comprehensive Analysis of Static, Buckling, and Free Vibration Behavior of Carbon Nanotube Reinforced Composite Plates on Pasternak’s Elastic Foundation

Vibrational analysis of polyurethane-sandwiched bridge decks with variable skew angles

Bridge decks are the surface of bridges that carry the weight of the vehicles and pedestrians crossing over them. The design of bridge decks varies depending on the span, traffic volume, and material availability. But nowadays, the need for a sustainable approach is required. So, use of a sustainable material for construction and retrofitting purposes is the need of the hour. In the present study, a novel synthetic material polyurethane has been used in bridges. The study deals with the variation in skew angles to determine the response of the bridge deck. The response of natural frequencies on the bridge deck due to the variation in skewness and thickness of steel are analysed under simply supported and clamped boundary conditions. Further, the bridge deck is sandwiched using steel and polyurethane having different thicknesses, and the responses are recorded. Afterwards, a bridge deck is modelled using polyurethane as a special case, to pursue sustainability and justify the RRR (reduce, reuse, and recycle) concept of waste management. A comparative study is also performed between the isotropic steel deck and sandwiched deck by varying the skewness. The skew angle is varied from 0° to 60° with a difference of 10°, i.e., 0°, 10°, 20°, 30°, 40°, 50°, and 60°. The frequencies of the isotropic steel and sandwiched decks are increasing when the skewness is increased. Also, the decks may be modelled in a way to enhances the vibration behaviour by sandwiching the existing steel decks. The free vibration frequencies of the sandwiched decks are comparable to the steel deck of similar thickness, which shows the use of polyurethane as the core material does not affect the vibrational characteristics of the deck, while at the same time reducing the cost significantly. The research lays the groundwork for the creation of engineering recommendations that practitioners can use.

A CO-HSDT isogeometric analysis for free vibration of matrix cracked FG-GPLRC plates coupled with stationary fluid

This paper for the first time proposes an efficiently C0-higer order shear deformation theory (HSDT) and isogeometric analysis (IGA) for the free vibration analysis of matrix cracked functionally graphene nanoplatelets reinforced composite (FG-GPLRC) plate coupled with stationary fluid. This case represents essential components of sophisticated structures utilized in industries such as shipbuilding, nuclear, marine, and naval. The properties of the four GPLs distributions of FG-GPLRC are evaluated by using a combination of the modified Halpin-Tsai micromechanics model and the rule of mixtures, while the degraded stiffness of cracked layers is predicted by the self-consistent micromechanical (SCM) model. The fluid is assumed to be homogeneous, inviscid, incompressible and irrotational, so the free-surface waves and hydrostatic pressure effects on structures are neglected. The governing equation of motion is derived by the Hamilton's principle, where three different fluid-plate interaction systems are taken into consideration. After validating the proposed method against existing literature, the effect of various parameters such as crack density, interaction boundary conditions (IBC), fluid level, GPLs distribution pattern, total number of layers, and geometric parameter on the free vibration of matrix cracked FG-GPLRC plate are investigated. It is believed that the finding in this paper may be helpful for the accurate design and analysis of matrix cracked FG-GPLRC plate submerged in fluid.

Free vibration of spinning stepped functionally graded circular cylindrical shells in a thermal environment

This paper investigates the free vibration of spinning stepped functionally graded material (FGM) circular cylindrical shells with general boundary conditions in a thermal environment. The artificial spring is implemented to simulate the general boundary constraints. Temperature-dependent material properties change constantly along the thickness direction. The Donnell-Mushtari shell theory is applied to derive the energy functions of thin stepped circular cylindrical shells, where the effect of centrifugal force and Coriolis force is taken into account. The modified Fourier-Ritz method is utilized to derive the frequency equations of the spinning stepped FGM circular cylindrical shells. The influences of spring stiffness, power-law index, and temperature on the traveling wave frequencies are investigated. The influence of configuration on the forward wave frequency and critical speed of three stepped shells, including the one-end thickened, the two-end thickened, and the middle-thickened stepped shells, is discussed. For each configuration, design strategies for the stepped shells are proposed.

Multiquadric Collocations for Nonlinear Vibration of Functionally Graded Plates of Ti–6Al–4V Metal

While Finite Element Method (FEM) has proven reliable for analyzing linear or nonlinear stresses in materials, structures, and fluid flows, its reliance on mesh generation can escalate project simulation costs. In contrast, mesh- free techniques offer an alternative by directly generating system algebraic equations for the entire issue domain, bypassing the need for a preset mesh. This study focuses on investigating the nonlinear free vibration response of shear-deformable Functionally Graded Material (FGM) plates. These plates are expected to exhibit varying material properties, following a power-law distribution linked to the volume fractions of constituent materials as plate thickness increases. Utilizing shear deformation theories and von Karman nonlinear kinematics, the study seeks a mathematical solution for the real physical issues encountered in these plates. To address these challenges, a meshless method employing the Multi Quadric Radial Basis Function (MQRBF) is employed for evaluation. The computed results reveal insights into how different material properties and amplitudes influence the nonlinear free vibration response of composite plates. Comparing these outcomes to prior research demonstrates promising progress in this area.

Free and forced vibration analysis of piezolaminated plates via an isogeometric layerwise finite element

Isogeometric layerwise finite element (L-IGA) formulation is a recent state-of-the-art approach integrating Non-Uniform Rational B-spline (NURBS) basis functions into the quasi-static solution process of piezolaminated composite plates. This study extends the application of the L-IGA framework to encompass free, forced vibration, and displacement control analyses of laminated composite plates with straight/curvilinear fibers and piezoelectric layers. To this end, the NURBS basis functions, utilized in geometry definition, are employed to solve electromechanically coupled differential equations following Hamilton’s variational principle. The adoption of high-order continuous NURBS shape functions throughout the IGA discretization span both in-plane and through-thickness laminate dimensions. This effectively facilitates precise geometry representation directly from Computer-Aided Design (CAD). Besides, such a discretization accelerates the convergence of displacement and electric potential solution fields toward exact results. Various benchmark problems have been solved to verify the robustness and high accuracy of the proposed dynamic L-IGA method. These include comparative analyses between L-IGA dynamic solutions (i.e. employing the Newmark-Beta method), analytical solutions, and ANSYS-Solid 226 finite element results. All the results are compared across various span-to-thickness ratios, mechanical-potential loading scenarios, and fiber orientation angles. Remarkably, the L-IGA method attains almost excellently accurate time response of various fields (displacement, stress, electric potential) and modal results, with considerably fewer mesh elements than Solid 226 solutions. Overall, such an outcome reveals the high potential and practical merits of the proposed L-IGA formulation as a proficient finite element approach for the dynamic analysis of piezolaminated plates.

Torsional vibration analysis and fuzzy adaptive PID control optimization of underwater vector propulsion shaft systems

To examine the torsional vibration of vector propulsion shaft system (VPSS), a four-degree-of-freedom vibration model of the VPSS is established by concentrated mass approach, and the torsional vibration differential equation of the VPSS is deduced based on the Lagrange approach. The vibration differential equations is addressed numerically applying the Runge-Kutta algorithm to investigate the effect of various working shaft angles β on the free and forced vibration of the VPSS under the excitation conditions. To further reduce the torsional vibration amplitude and avoid fatigue damage of the system, and considering the nonlinear relationship within the system, this study develops a fuzzy adaptive PID approach to control the VPSS. The results show that the maximum torsional vibration amplitude of the VPSS is reduced by more than 70% and the transient response time is shortened by more than 90% with this control approach, which effectively reduces the torsional vibration amplitude of the VPSS and thereby significantly improves the safety performance of the underwater vehicle. This may provide technical references for the vibration control theory of the VPSS as well as engineering applications.

Study on MHD Pulses, Waves, and Instability in Trigging multiple renewables noise on various spectral information scales

Major concepts covered in this research include: State of being free vibration and method start changing; MHD waveguides like the magnetic properties dorsal fin, radicular groups, and radicular streaming sites; processes for frequency supplied in imperativeness overflows throughout sub hurricanes and solar activity; the possibility of Heat diffusion resonant frequencies along empty field lines; potential motorists of MHD waves; diagnostic tools of plasma screens with MHD waves; the collaboration of MHD waves mostly with positive ions limits (ionosphere and chromosphere). This review is directed largely at experts in the subjects of magnetosphere material science and solar theoretical physics, while it does delve into the intricacies of the surround investigation fields to those who are concerned. Though there are several noise contributors, aerodynamics is the most significant. When it concerns to aerodynamics noise, the distal end of blades of wind turbines is where the majority of the action occurs. A subject of this research is on blade tip noise caused by wind generators, and an evaluation and comparison of the many methods being used and researched to minimize this difficulty is the paper's primary focus. Subjective assessment outcomes are also compared to quantifiable measurements. Several methods are proposed, and the risks and benefits are compared. Among the most intriguing instances of plasma in reality that we're able to examine close quarters are really the Solar energy, Atmosphere's geomagnetic, and stratosphere. Were very could be used to model such plasmas effectively in principle (MHD). In MHD, the statistics and dynamics of liquids that conduct electricity are hypothetically characterized.

Free vibration analysis of an O-pattern graphene reinforced axial functionally graded polymer matrix nano-composite non-uniform beam

Recently, the demand for nanocomposites in the form of functionally graded materials (FGM) has increased because of their improved weight-to-stiffness ratios, less delamination effects, and ability to have desired qualities at the right location. Additionally, compared to typical composites, static qualities like strength and elasticity are superior. In this research work, a model for an axially graphene-reinforced functionally graded polymer matrix nanocomposite non-uniform beam is prepared, to obtain the dynamic behavior of the beam in form of its Natural Frequencies. Along the length of the beam, the graphene Nano reinforcement is dispersed in an epoxy polymer matrix as “O” pattern using a function. Material modulus at each location of the beam is modelled using Halpin-Tsai micromechanics theory, the mass density and Poisson’s Ratio of the beam are determined using rule of mixture. The geometry non-uniformity of the beam is modelled using an exponential function. Using MATLAB software code, simulation and parametric analysis of the beam are performed for various slenderness ratios and varied boundary conditions. The non-uniform beam result is obtained after the result for a uniform beam is used to validate it. In result it is analyzed that for the particular geometric and reinforcement configuration of the beam, as the non-uniformity in the beam geometry is increases, the fundamental frequency decreases, and the slenderness ratio has also the same effect on its fundamental frequency.

Free vibration analyses of 3D printed plates with different geometric fillings: experimental testing and numerical simulations

Abstract In this article, the numerical and experimental free vibration analyses of PLA-based composite plates with different filling geometries were carried out. Firstly, the natural frequencies and modal shapes were obtained from finite element (FE) methods to characterize the vibration behavior of the plates. The obtained results were compared with experimental testing of the three-dimensional (3D) produced plates. In the comparison, it was seen that the finite element analysis and the experimental results were quite close to each other. It was also observed that the highest frequencies are measured by a triangle, then the grid and honeycomb. Moreover, higher frequencies and lower weights are possible with the triangle pattern fill. On the other hand, it is noted that the types of filling structures do not affect the modal shapes of the 3D plates. Thus, the results of this paper are of utmost importance for getting light structure and high frequencies.

Seismic analysis of Islamic Egyptian minarets through 3D scanning and dynamic simulation

Recently, Egypt had seismic activity. These seismic events have affected the stability of minarets, especially historical ones. Weight is one of the minaret's main stability factors. The main objective of the current research is to perform a three-dimensional (3D) assessment of an existing minaret, determine its accurate spatial model, document its current condition, examine its stability in the event of earthquakes, and identify the requisite measures to safeguard the minaret from any potential damage. The masonry to construct the minaret was used by extracting and examining specimens of this substance to determine its physical characteristics. The current work created three-dimensional models of the Abou-Ghanam El-Bialy minaret using a terrestrial laser scanner (TLS) to document its current condition, as well as minaret was subjected to a free vibration analysis using 3D finite element modeling. Finally, the minaret's seismic behavior was assessed utilizing mode forms, base responses, and normal stresses. The surveying method effectively documented the Minarets' existing case. The 3D seismic analysis showed that the minaret responded dynamically to earthquake loading, with mode shapes, base reactions, and normal stresses being crucial characteristics. Based on these data, we may suggest procedures to protect the minaret during seismic events.

An exact analytical solution for coupled vibration analysis of a piezoelectric resonator

Abstract Piezoelectric resonators are widely used as the active components in devices such as sensors, actuators, communication filters, and micro/nano-electro-mechanical systems (MEMS / NEMS). Due to the piezoelectric effect, Poisson’s ratio, and its finite dimension, the thickness and lateral vibration modes in a piezoelectric resonator are inevitably coupled. In this paper, an exact analytical model for coupled vibration analysis of a piezoceramic disk is developed based on a new superstition method. The free vibrations are decomposed into thickness and lateral directions in a new form of Fourier-Bessel series and then they are superimposed to satisfy the boundary conditions. To verify the validity of the analytical model proposed here, numerical simulations are performed using COMSOL Multiphysics. An excellent agreement is observed. This analytical model can be applied to the design and optimization of piezoelectric devices.

A new modified Bessel‐type radial basis function for meshless methods: Utilized in the analysis of free vibration in 2D functionally graded Euler–Bernoulli beams

AbstractRadial basis functions (RBFs) are extensively employed in mesh‐free methods owing to their distinct properties. This study presents a novel RBF formulation based on a modified first‐kind Bessel function, introduced for the first time. The efficacy and precision of the proposed function are assessed through an examination of the free vibrations of Euler–Bernoulli beams composed of two‐directional functionally graded materials. Longitudinal and thickness property variations are modeled in polynomial and exponential forms, respectively. The performance of the novel RBF is scrutinized under various boundary conditions (clamped, simply supported, and free), and comparative analyses are conducted against similar investigations and an RBF based on the first‐kind Bessel function. Convergence analysis of the proposed modified first‐kind Bessel function‐based RBF reveals superior convergence rates compared to the first‐kind Bessel function‐based RBF. Moreover, a comparison between results obtained from modeling using the proposed RBF and exact solutions underscores the adequacy of this approach, with a maximum discrepancy of 4.933% observed under clamped‐free boundary conditions. In essence, the findings suggest that the proposed modified first‐kind Bessel function‐based RBF holds promise for analyzing the free vibrations of functionally graded Euler–Bernoulli beams. The primary aim of this research is to introduce and validate a new RBF based on a modified first‐kind Bessel function for the analysis of free vibrations in Euler–Bernoulli beams made of two‐directional functionally graded materials. The study focuses on evaluating the performance and accuracy of this novel RBF in comparison with existing RBFs and exact solutions. By addressing the limitations of conventional RBFs and proposing an innovative approach, this research aims to enhance the accuracy and efficiency of meshless methods in structural vibration analysis.

Experimental and numerical analyses on the modal behaviour of an aluminium alloy sheet

Abstract The study of modal behaviour for vehicle body panels represents a field of interest for automotive engineering, having a major influence on automotive comfort, with respect to vehicle noise, vibration and harshness, but also concerning the durability of vehicle body. The investigation of natural frequencies and vibration mode shapes is crucial in the design phase, because essential information can be obtained concerning the behaviour of the components in dynamic conditions. The current paper focuses on the investigation of vibration modes and frequency response function on an aluminium alloy sheet. The aim of the paper is to perform the study of modal behaviour both experimentally and theoretically, through measurements using the impact hammer method and respectively through finite element analysis. The CAD model of the aluminium alloy sheet has been developed in Catia V5 environment in view of elaborating the finite element model, which has been used for investigation of modal behaviour, taking into account the case of free vibrations. Through the modal finite element analysis performed in Ansys Workbench, the natural frequencies of the aluminium alloy sheet, as well as the corresponding mode shapes have been obtained. Experiments have been performed on an aluminium alloy sheet, mounted on an elastic support with low natural frequency. The impact hammer method has been used for obtaining the natural frequencies, through frequency analysis of accelerations measured with two piezoelectric accelerometers mounted on the aluminium alloy sheet. The frequency response function has been computed from the response acceleration measured on the aluminium alloy sheet and the impact force measured using the force transducer of the impact hammer. Virtual instruments have been developed in LabVIEW environment for data acquisition, time domain and frequency analysis, as well as for determining the frequency response function using the measured signals. The natural frequencies obtained from the finite element analyses have been compared to the results of measurements and very good similarities have been ascertained. The experimental investigation of modal behaviour contributed to the validation of the finite element model, but further research is required to investigate the possibilities of improving the modal behaviour of the aluminium alloy sheet.

Study on the effect of the excited area on the vibration characteristics of a thin circular plate

Abstract In this paper, the vibration modes and radiated directivity of a thin circular plate excited by a sandwich longitudinal vibration transducer are studied. The finite element model is set up to study the effect of the contact area between the transducer and the circular radiation plate on the vibration modes and the radiation characteristics. The first six vibration modes of the thin vibration plate are analyzed, and the results show that the vibration modes of the area-excited thin circular plate are different from those of the free vibration thin circular plate and the point-excited thin circular plate. Simulation results show that under different contact areas, the thin circular plate vibrates in different modes. With the increase of the excitation area, the frequencies of each mode of the circular plate gradually increase. Moreover, the excited area also affects the radiative directivity. With the increase of the excited area, the main lobe width of the radiative directivity becomes narrower.